Problem
The round off errors when measuring the distance that a long jumper has jumped is uniformly distributed between 0 and $5.4 \mathrm{~mm}$. Round values to 4 decimal places when possible.
a. The mean of this distribution is
b. The standard deviation is
c. The probability that the round off error for a jumper's distance is exactly 0.9 is $P(x=0.9)=$
d. The probability that the round off error for the distance that a long jumper has jumped is between 0 and $5.4 \mathrm{~mm}$ is $P(0.82.08)=$
f. $P(x>4.1 \mid x>1.6)=$
g. Find the 24 th percentile.
h. Find the maximum for the lower quartile.
Solution
Step 1 ：The mean of a uniform distribution is calculated as the sum of the minimum and maximum values divided by 2. In this case, the minimum value is 0 and the maximum value is 5.4 mm. So, the mean is \( \frac{0 + 5.4}{2} \).
Step 2 ：Calculate the mean: \( \frac{0 + 5.4}{2} = 2.7 \).
Step 3 ：Final Answer: The mean of this distribution is \(\boxed{2.7}\).
